The advent of information and combinatorial complexity: - - PowerPoint PPT Presentation

The advent of information and combinatorial complexity: Understanding Darwinian evolution at the molecular level Peter Schuster

Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA

ESF-COST Conference on Systems Chemistry Acquafredda di Maratea, 03.– 08.10.2008

Web-Page for further information: http://www.tbi.univie.ac.at/~pks

What is information ?

• Information is (only) what is understood.
• Information is (only) what creates information.

Carl Friedrich von Weizsäcker, 1912-2007, German physicist and philosopher.

Information in biology

• Understanding of information is interpreted as decoding,
• maintenance of information requires reproduction, and
• creation of information occurs through adaptation to the

environment by means of a Darwinian mechanism of variation and selection.

1. Requirements for information processing 2. The chemistry of Darwinian evolution 3. RNA sequences and structures 4. Consequences of neutrality 5. Evolutionary optimization of RNA structure

• 1. Requirements for information processing

2. The chemistry of Darwinian evolution 3. RNA sequences and structures 4. Consequences of neutrality 5. Evolutionary optimization of RNA structure

Classification of purine- pyrimidine base pairs

Classification of purine-purine base pairs

Classification of pyrimidine- pyrimidine base pairs

General classification of base pairs

N.B. Leontis and E. Westhof, RNA 7:499-512 (2001)

James D. Watson, 1928-, and Francis H.C. Crick, 1916-2004 Nobel prize 1962

1953 – 2003 fifty years double helix The three-dimensional structure of a short double helical stack of B-DNA

C G ``A´´ U

2,6-diamino purine 2-keto, 6-amino purine 2,6-diketo purine 5-keto, 7-amino, 1,6,8-triaza indolicine 5- , 7- , 1,6,8-triaza indolicine amino keto 2-amino,6-keto purine 2-keto, 4-amino pyrimidine

2- , 4- pyrimidine amino keto

2,4-di pyrimidine keto 2,6-diamin pyrimidine

• 2-

, 6-keto pyrazine amino 2- , 6- pyrazine keto amino

Color code: Donor—Acceptor Acceptor—Donor

Hydrogen bonding patterns for Watson- Crick base pairs

S.A. Benner et al., Reading the palimpsest: Contemporary biochemical data and the RNA world. In: R.F.Gesteland and J.F.Atkins, eds. The RNA World, pp.27-70. CSHL Press, 1993

Canonical Watson-Crick base pairs: cytosine – guanine uracil – adenine

W.Saenger, Principles of Nucleic Acid Structure, Springer, Berlin 1984

4n different sequences for chain length n n = 100: 4100 = 1.6 1060 sequences

Combinatorial complexity in biopolymer sequences

Information processing requires digitalization in the sense of „yes-or-no“ decisions. Nature solves the problem through complementarity of nucleobases:

• Biological information storage in nucleic acids is extremely

specific through applying the straightforward stereochemistry

• f the double helix.
• Biological information processing is overcoming thermodynamic

restrictions without violating its rules.

• Digitalization of biological information is the key towards easily

accessible combinatorial complexity and provides the basis for the inexhaustible reservoir of genotypes and shapes in nature.

1. Requirements for information processing

• 2. The chemistry of Darwinian evolution

3. RNA sequences and structures 4. Consequences of neutrality 5. Evolutionary optimization of RNA structure

Three necessary conditions for Darwinian evolution are: 1. Multiplication, 2. Variation, and 3. Selection. Variation through mutation and recombination operates on the genotype whereas the phenotype is the target of selection. One important property of the Darwinian scenario is that variations in the form of mutations or recombination events occur uncorrelated with their effects on the selection process. All conditions can be fulfilled not only by cellular organisms but also by nucleic acid molecules in suitable cell-free experimental assays.

DNA structure and DNA replication

‚Replication fork‘ in DNA replication The mechanism of DNA replication is ‚semi-conservative‘

Complementary replication is the simplest copying mechanism

• f RNA.

Complementarity is determined by Watson-Crick base pairs: GC and A=U

Kinetics of RNA replication

C.K. Biebricher, M. Eigen, W.C. Gardiner, Jr. Biochemistry 22:2544-2559, 1983

1 1 2 2 2 1

and x f dt dx x f dt dx = =

2 1 2 1 2 1 2 1 2 1 2 1

, , , , f f f f x f x = − = + = = = ξ ξ η ξ ξ ζ ξ ξ

ft ft

e t e t ) ( ) ( ) ( ) ( ζ ζ η η = =

−

Complementary replication as the simplest molecular mechanism of reproduction

A point mutation is caused by an incorrect incorporation of a nucleobase into the growing chain during replication. Replication and mutation are parallel chemical reactions.

Evolution of RNA molecules based on Qβ phage

D.R.Mills, R.L.Peterson, S.Spiegelman, An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule. Proc.Natl.Acad.Sci.USA 58 (1967), 217-224 S.Spiegelman, An approach to the experimental analysis of precellular evolution. Quart.Rev.Biophys. 4 (1971), 213-253 C.K.Biebricher, Darwinian selection of self-replicating RNA molecules. Evolutionary Biology 16 (1983), 1-52 G.Bauer, H.Otten, J.S.McCaskill, Travelling waves of in vitro evolving RNA. Proc.Natl.Acad.Sci.USA 86 (1989), 7937-7941 C.K.Biebricher, W.C.Gardiner, Molecular evolution of RNA in vitro. Biophysical Chemistry 66 (1997), 179-192 G.Strunk, T.Ederhof, Machines for automated evolution experiments in vitro based on the serial transfer concept. Biophysical Chemistry 66 (1997), 193-202 F.Öhlenschlager, M.Eigen, 30 years later – A new approach to Sol Spiegelman‘s and Leslie Orgel‘s in vitro evolutionary studies. Orig.Life Evol.Biosph. 27 (1997), 437-457

RNA sample Stock solution: Q RNA-replicase, ATP, CTP, GTP and UTP, buffer

• Time

1 2 3 4 5 6 69 70

Application of serial transfer to RNA evolution in the test tube

Chemical kinetics of molecular evolution

• M. Eigen, P. Schuster, `The Hypercycle´, Springer-Verlag, Berlin 1979

Chemical kinetics of replication and mutation as parallel reactions

Quasispecies

Driving virus populations through threshold

The error threshold in replication

Molecular evolution of viruses

A fitness landscape showing an error threshold

Quasispecies as a function of the mutation rate p f0 = = 10 Single peak fitness landscape: 1 and

2 1

= = = =

N

f f f f f K

n N i i i

N I x f x f κ σ = − =

∑ =

; sequence master ) 1 (

1

K

Fitness landscapes showing error thresholds

Error threshold: Individual sequences n = 10, = 2 and d = 0, 1.0, 1.85

Evolutionary design of RNA molecules

A.D. Ellington, J.W. Szostak, In vitro selection of RNA molecules that bind specific ligands. Nature 346 (1990), 818-822

• C. Tuerk, L. Gold, SELEX - Systematic evolution of ligands by exponential enrichment: RNA

ligands to bacteriophage T4 DNA polymerase. Science 249 (1990), 505-510 D.P. Bartel, J.W. Szostak, Isolation of new ribozymes from a large pool of random sequences. Science 261 (1993), 1411-1418 R.D. Jenison, S.C. Gill, A. Pardi, B. Poliski, High-resolution molecular discrimination by RNA. Science 263 (1994), 1425-1429

• Y. Wang, R.R. Rando, Specific binding of aminoglycoside antibiotics to RNA. Chemistry &

Biology 2 (1995), 281-290

• L. Jiang, A. K. Suri, R. Fiala, D. J. Patel, Saccharide-RNA recognition in an aminoglycoside

antibiotic-RNA aptamer complex. Chemistry & Biology 4 (1997), 35-50

An example of ‘artificial selection’ with RNA molecules or ‘breeding’ of biomolecules

tobramycin RNA aptamer, n = 27

Formation of secondary structure of the tobramycin binding RNA aptamer with KD = 9 nM

• L. Jiang, A. K. Suri, R. Fiala, D. J. Patel, Saccharide-RNA recognition in an aminoglycoside antibiotic-

RNA aptamer complex. Chemistry & Biology 4:35-50 (1997)

Application of molecular evolution to problems in biotechnology

Artificial evolution in biotechnology and pharmacology G.F. Joyce. 2004. Directed evolution of nucleic acid enzymes. Annu.Rev.Biochem. 73:791-836.

• C. Jäckel, P. Kast, and D. Hilvert. 2008. Protein design by

directed evolution. Annu.Rev.Biophys. 37:153-173. S.J. Wrenn and P.B. Harbury. 2007. Chemical evolution as a tool for molecular discovery. Annu.Rev.Biochem. 76:331-349.

Results from kinetic theory of molecular evolution and evolution experiments:

• Evolutionary optimization does not require cells and occurs as

well in cell-free molecular systems.

• Replicating ensembles of molecules form stationary populations

called quasispecies, which represent the genetic reservoir of asexually reproducing species.

• For stable inheritance of genetic information mutation rates

must not exceed a precisely defined and computable error- threshold.

• The error-threshold can be exploited for the development of

novel antiviral strategies.

• In vitro evolution allows for production of molecules for

predefined purposes and gave rise to a branch of biotechnology.

1. Requirements for information processing 2. The chemistry of Darwinian evolution

• 3. RNA sequences and structures

4. Consequences of neutrality 5. Evolutionary optimization of RNA structure

RNA folding determination of RNA function molecular recognition catalysis binding to: ground state transition state aptamers ribozymes

The paradigm of structural biology

O CH2 OH O O P O O O

N1

O CH2 OH O P O O O

N2

O CH2 OH O P O O O

N3

O CH2 OH O P O O O

N4

N A U G C

k =

, , ,

3' - end 5' - end Na Na Na Na

5'-end 3’-end

GCGGAU AUUCGC UUA AGUUGGGA G CUGAAGA AGGUC UUCGAUC A ACCA GCUC GAGC CCAGA UCUGG CUGUG CACAG

Definition of RNA structure

N = 4n NS < 3n Criterion: Minimum free energy (mfe) Rules: _ ( _ ) _ {AU,CG,GC,GU,UA,UG} A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs

What is neutrality ?

Selective neutrality = = several genotypes having the same fitness. Structural neutrality = = several genotypes forming molecules with the same structure.

Reference for postulation and in silico verification of neutral networks

many genotypes

• ne phenotype

AUCAAUCAG GUCAAUCAC GUCAAUCAU GUCAAUCAA G U C A A U C C G G U C A A U C G G GUCAAUCUG G U C A A U G A G G U C A A U U A G GUCAAUAAG GUCAACCAG G U C A A G C A G GUCAAACAG GUCACUCAG G U C A G U C A G GUCAUUCAG GUCCAUCAG GUCGAUCAG GUCUAUCAG GUGAAUCAG GUUAAUCAG GUAAAUCAG GCCAAUCAG GGCAAUCAG GACAAUCAG UUCAAUCAG CUCAAUCAG

GUCAAUCAG

One-error neighborhood

The surrounding of GUCAAUCAG in sequence space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

GGCUAUCGUAUGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUAGACG GGCUAUCGUACGUUUACUCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGCUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCCAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUGUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAACGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCUGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCACUGGACG GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGUCCCAGGCAUUGGACG GGCUAGCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCGAAAGUCUACGUUGGACCCAGGCAUUGGACG GGCUAUCGUACGUUUACCCAAAAGCCUACGUUGGACCCAGGCAUUGGACG

G G C U A U C G U A C G U U U A C C C AA AAG UC UACG U UGGA CC C A GG C A U U G G A C G

One error neighborhood – Surrounding of an RNA molecule of chain length n=50 in sequence and shape space

Number Mean Value Variance Std.Dev. Total Hamming Distance: 150000 11.647973 23.140715 4.810480 Nonzero Hamming Distance: 99875 16.949991 30.757651 5.545958 Degree of Neutrality: 50125 0.334167 0.006961 0.083434 Number of Structures: 1000 52.31 85.30 9.24 1 (((((.((((..(((......)))..)))).))).))............. 50125 0.334167 2 ..(((.((((..(((......)))..)))).)))................ 2856 0.019040 3 ((((((((((..(((......)))..)))))))).))............. 2799 0.018660 4 (((((.((((..((((....))))..)))).))).))............. 2417 0.016113 5 (((((.((((.((((......)))).)))).))).))............. 2265 0.015100 6 (((((.(((((.(((......))).))))).))).))............. 2233 0.014887 7 (((((..(((..(((......)))..)))..))).))............. 1442 0.009613 8 (((((.((((..((........))..)))).))).))............. 1081 0.007207 9 ((((..((((..(((......)))..))))..)).))............. 1025 0.006833 10 (((((.((((..(((......)))..)))).))))).............. 1003 0.006687 11 .((((.((((..(((......)))..)))).))))............... 963 0.006420 12 (((((.(((...(((......)))...))).))).))............. 860 0.005733 13 (((((.((((..(((......)))..)))).)).)))............. 800 0.005333 14 (((((.((((...((......))...)))).))).))............. 548 0.003653 15 (((((.((((................)))).))).))............. 362 0.002413 16 ((.((.((((..(((......)))..)))).))..))............. 337 0.002247 17 (.(((.((((..(((......)))..)))).))).).............. 241 0.001607 18 (((((.(((((((((......))))))))).))).))............. 231 0.001540 19 ((((..((((..(((......)))..))))...))))............. 225 0.001500 20 ((....((((..(((......)))..)))).....))............. 202 0.001347 G G C U A U C G U A C G U U U A C C C AA AAG UC UACG U UGGA CC C A GG C A U U G G A C G

Shadow – Surrounding of an RNA structure in shape space: AUGC alphabet, chain length n=50

1. Requirements for information processing 2. The chemistry of Darwinian evolution 3. RNA sequences and structures

• 4. Consequences of neutrality

5. Evolutionary optimization of RNA structure

Charles Darwin. The Origin of Species. Sixth edition. John Murray. London: 1872

Motoo Kimuras population genetics of neutral evolution. Evolutionary rate at the molecular level. Nature 217: 624-626, 1955. The Neutral Theory of Molecular Evolution. Cambridge University Press. Cambridge, UK, 1983.

The average time of replacement of a dominant genotype in a population is the reciprocal mutation rate, 1/, and therefore independent of population size.

Is the Kimura scenario correct for frequent mutations?

dH = 1

5 . ) ( ) ( lim

2 1

= =

→

p x p x

p

dH = 2

a p x a p x

p p

− = =

→ →

1 ) ( lim ) ( lim

2 1

dH ≥3

random fixation in the sense of Motoo Kimura Pairs of genotypes in neutral replication networks

for comparison: = 0, = 1.1, d = 0

Neutral network: Individual sequences n = 10, = 1.1, d = 1.0

Consensus sequence of a quasispecies of two strongly coupled sequences of Hamming distance dH(Xi,,Xj) = 1.

Neutral network: Individual sequences n = 10, = 1.1, d = 1.0

Consensus sequence of a quasispecies of two strongly coupled sequences of Hamming distance dH(Xi,,Xj) = 2.

N = 7

Computation of sequences in the core of a neutral network

N = 7 Neutral networks with increasing : = 0.10, s = 229

N = 24 Neutral networks with increasing : = 0.15, s = 229

N = 70 Neutral networks with increasing : = 0.20, s = 229

Extension of the notion of structure

Extension of the notion of structure

mfe-weight: 0.7196

GGCCCCUUUGGGGGCCAGACCCCUAAAGGGGUC ((((((((((((((.....)))))))))))))) -26.30 ((((((....)))))).((((((....)))))) -25.30 .(((((((((((((.....))))))))))))). -24.80 (((((((((((((.......))))))))))))) -24.50 ((((((....)))))).(((((......))))) -23.40 (((((......))))).((((((....)))))) -23.30 ..((((((((((((.....)))))))))))).. -23.10 (((((((((((((......)))).))))))))) -23.00 .((((((((((((.......)))))))))))). -23.00 (((((((.((((((.....)))))).))))))) -22.80 ((((((((.(((((.....))))).)))))))) -22.70 ((((((....))))))..(((((....))))). -22.70 ((((((.(((((((.....))))))).)))))) -22.20 (((((((((.((((.....)))).))))))))) -22.10 (.((((((((((((.....)))))))))))).) -21.90 .(((((((((((((.....)))))))))))).) -21.90 ((((((....))))))...((((....)))).. -21.60 (((((((..(((((.....)))))..))))))) -21.50 .((((((((((((......)))).)))))))). -21.50 (((((......))))).(((((......))))) -21.40 .((((((.((((((.....)))))).)))))). -21.30 ..(((((((((((.......))))))))))).. -21.30

Suboptimal structures and partition function

• f a small RNA molecule: n = 33

GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAUUGGACG (((((.((((..(((......)))..)))).))).))............. -7.30 ..........((((((.((....((((.....))))...))...)))))) -6.70 ..........((((((.((....(((((...)))))...))...)))))) -6.60 ..(((.((((..(((......)))..)))).)))..((((...))))... -6.10 (((((.((((..(((......)))..)))).))).))..(........). -6.00 (((((.((((..((........))..)))).))).))............. -6.00 .(((.((..((((..((......))..))))..))....)))........ -6.00 GGCUAUCGUACGUUUACACAAAAGUCUACGUUGGACCCAGGCAUUGGACG (((((.((((..(((......)))..)))).))).))............. -7.30 .(((.((..((((..((......))..))))..))....)))........ -6.50 .(((.....((((..((......))..))))((....)))))........ -6.30 ..(((.((((..(((......)))..)))).)))..((((...))))... -6.10 (((((.((((..(((......)))..)))).))).))..(........). -6.00 (((((.((((..((........))..)))).))).))............. -6.00 .(((...((((((..((......))..))))...))...)))........ -6.00 GGCUAUCGUACGUUUACCCAAAAGUCUACGUUGGACCCAGGCAAUGGACG (((((.((((..(((......)))..)))).))).))............. -7.30 ..(((.((((..(((......)))..)))).)))..(((.....)))... -7.20 ..........((((((.((....((((.....))))...))...)))))) -6.70 ..........((((((.((....(((((...)))))...))...)))))) -6.60 (((((.((((..(((......)))..)))).))).))((.....)).... -6.50 (.(((.((((..(((......)))..)))).))).)(((.....)))... -6.30 .((((.((((..(((......)))..)))).))).)(((.....)))... -6.30 .....(((.((((..((......))..)))))))..(((.....)))... -6.30 (.(((.((((..(((......)))..)))).)))..(((.....))).). -6.10 .....((..((((..((......))..))))..)).(((.....)))... -6.10 ......(((.((((...((....((((.....))))...)).)))).))) -6.10 (((((.((((..(((......)))..)))).))).))..(........). -6.00 (((((.((((..((........))..)))).))).))............. -6.00 .(((.((..((((..((......))..))))..))....)))........ -6.00 ......(((.((((...((....(((((...)))))...)).)))).))) -6.00

Extension of the notion of structure

Extension of the notion of structure

JN1LH

1D 1D 1D 2D 2D 2D R R R

G GGGUGGAAC GUUC GAAC GUUCCUCCC CACGAG CACGAG CACGAG

• 28.6 kcal·mol
• 1

G/

• 31.8 kcal·mol
• 1

G G G G G G C C C C C C A A U U U U G G C C U U A A G G G C C C A A A A G C G C A A G C /G

• 28.2 kcal·mol
• 1

G G G G G G GG CCC C C C C C U G G G G C C C C A A A A A A A A U U U U U G G C C A A

• 28.6 kcal·mol
• 1

3 3 3 13 13 13 23 23 23 33 33 33 44 44 44

5' 5' 3’ 3’

J.H.A. Nagel, C. Flamm, I.L. Hofacker, K. Franke, M.H. de Smit, P. Schuster, and C.W.A. Pleij. Structural parameters affecting the kinetic competition of RNA hairpin formation. Nucleic Acids Res. 34:3568-3576, 2006.

An RNA switch

A ribozyme switch

E.A.Schultes, D.B.Bartel, Science 289 (2000), 448-452

Two ribozymes of chain lengths n = 88 nucleotides: An artificial ligase (A) and a natural cleavage ribozyme of hepatitis--virus (B)

The sequence at the intersection: An RNA molecules which is 88 nucleotides long and can form both structures

Two neutral walks through sequence space with conservation of structure and catalytic activity

RNA 9:1456-1463, 2003

Evidence for neutral networks and shape space covering

Evidence for neutral networks and intersection of apatamer functions

Neutrality in molecular structures and its role in evolution:

• Neutrality is an essential feature in biopolymer structures at the

resolution that is relevant for function.

• Neutrality manifests itself in the search for minimum free energy

structures.

• Diversity in function despite neutrality in structures results from

differences in suboptimal conformations and folding kinetics.

• Neutrality is indispensible for optimization and adaptation.

1. Requirements for information processing 2. The chemistry of Darwinian evolution 3. RNA sequences and structures 4. Consequences of neutrality

• 5. Evolutionary optimization of RNA structure

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution of RNA molecules as a Markow process and its analysis by means of the relay series

Evolution in silico

• W. Fontana, P. Schuster,

Science 280 (1998), 1451-1455

Phenylalanyl-tRNA as target structure Structure of randomly chosen initial sequence

Replication rate constant (Fitness): fk = / [ + dS

(k)]

dS

(k) = dH(Sk,S)

Selection pressure: The population size, N = # RNA moleucles, is determined by the flux: Mutation rate: p = 0.001 / Nucleotide Replication N N t N ± ≈ ) ( The flow reactor as a device for studying the evolution of molecules in vitro and in silico.

In silico optimization in the flow reactor: Evolutionary Trajectory

28 neutral point mutations during a long quasi-stationary epoch Transition inducing point mutations change the molecular structure Neutral point mutations leave the molecular structure unchanged

Neutral genotype evolution during phenotypic stasis

Randomly chosen initial structure Phenylalanyl-tRNA as target structure

Evolutionary trajectory Spreading of the population

• n neutral networks

Drift of the population center in sequence space

Spreading and evolution of a population on a neutral network: t = 150

Spreading and evolution of a population on a neutral network : t = 170

Spreading and evolution of a population on a neutral network : t = 200

Spreading and evolution of a population on a neutral network : t = 350

Spreading and evolution of a population on a neutral network : t = 500

Spreading and evolution of a population on a neutral network : t = 650

Spreading and evolution of a population on a neutral network : t = 820

Spreading and evolution of a population on a neutral network : t = 825

Spreading and evolution of a population on a neutral network : t = 830

Spreading and evolution of a population on a neutral network : t = 835

Spreading and evolution of a population on a neutral network : t = 840

Spreading and evolution of a population on a neutral network : t = 845

Spreading and evolution of a population on a neutral network : t = 850

Spreading and evolution of a population on a neutral network : t = 855

A sketch of optimization on neutral networks

Is the degree of neutrality in GC space much lower than in AUGC space ? Statistics of RNA structure optimization: P. Schuster, Rep.Prog.Phys. 69:1419-1477, 2006

Number Mean Value Variance Std.Dev. Total Hamming Distance: 150000 11.647973 23.140715 4.810480 Nonzero Hamming Distance: 99875 16.949991 30.757651 5.545958 Degree of Neutrality: 50125 0.334167 0.006961 0.083434 Number of Structures: 1000 52.31 85.30 9.24 1 (((((.((((..(((......)))..)))).))).))............. 50125 0.334167 2 ..(((.((((..(((......)))..)))).)))................ 2856 0.019040 3 ((((((((((..(((......)))..)))))))).))............. 2799 0.018660 4 (((((.((((..((((....))))..)))).))).))............. 2417 0.016113 5 (((((.((((.((((......)))).)))).))).))............. 2265 0.015100 6 (((((.(((((.(((......))).))))).))).))............. 2233 0.014887 7 (((((..(((..(((......)))..)))..))).))............. 1442 0.009613 8 (((((.((((..((........))..)))).))).))............. 1081 0.007207 9 ((((..((((..(((......)))..))))..)).))............. 1025 0.006833 10 (((((.((((..(((......)))..)))).))))).............. 1003 0.006687 11 .((((.((((..(((......)))..)))).))))............... 963 0.006420 12 (((((.(((...(((......)))...))).))).))............. 860 0.005733 13 (((((.((((..(((......)))..)))).)).)))............. 800 0.005333 14 (((((.((((...((......))...)))).))).))............. 548 0.003653 15 (((((.((((................)))).))).))............. 362 0.002413 16 ((.((.((((..(((......)))..)))).))..))............. 337 0.002247 17 (.(((.((((..(((......)))..)))).))).).............. 241 0.001607 18 (((((.(((((((((......))))))))).))).))............. 231 0.001540 19 ((((..((((..(((......)))..))))...))))............. 225 0.001500 20 ((....((((..(((......)))..)))).....))............. 202 0.001347 Number Mean Value Variance Std.Dev. Total Hamming Distance: 50000 13.673580 10.795762 3.285691 Nonzero Hamming Distance: 45738 14.872054 10.821236 3.289565 Degree of Neutrality: 4262 0.085240 0.001824 0.042708 Number of Structures: 1000 36.24 6.27 2.50 1 (((((.((((..(((......)))..)))).))).))............. 4262 0.085240 2 ((((((((((..(((......)))..)))))))).))............. 1940 0.038800 3 (((((.(((((.(((......))).))))).))).))............. 1791 0.035820 4 (((((.((((.((((......)))).)))).))).))............. 1752 0.035040 5 (((((.((((..((((....))))..)))).))).))............. 1423 0.028460 6 (.(((.((((..(((......)))..)))).))).).............. 665 0.013300 7 (((((.((((..((........))..)))).))).))............. 308 0.006160 8 (((((.((((..(((......)))..)))).))))).............. 280 0.005600 9 (((((.((((..(((......)))..)))).))).))...(((....))) 278 0.005560 10 (((((.(((...(((......)))...))).))).))............. 209 0.004180 11 (((((.((((..(((......)))..)))).))).)).(((......))) 193 0.003860 12 (((((.((((..(((......)))..)))).))).))..(((.....))) 180 0.003600 13 (((((.((((..((((.....)))).)))).))).))............. 180 0.003600 14 ..(((.((((..(((......)))..)))).)))................ 176 0.003520 15 (((((.((((.((((.....))))..)))).))).))............. 175 0.003500 16 ((((( (((( ((( ))) ))))))))) 167 0 003340

G G C U A U C G U A C G U U U A C C C AA AAG UC UACG U UGGA CC C A GG C A U U G G A C G C C C C G G G C C G G G G G C G C G C GG GCC GG CGGC G CGGC GG G G GG G G G G C G G C C

Shadow – Surrounding of an RNA structure in shape space – AUGC and GC alphabet

Neutrality in evolution

Charles Darwin: „ ... neutrality might exist ...“ Motoo Kimura: „ ... neutrality is unaviodable and represents the main reason for changes in genotypes and leads to molecular phylogeny ...“ Current view: „ ... neutrality is essential for successful

• ptimization on rugged landscapes ...“

Proposed view: „ ... neutrality provides the genetic reservoir for functions in the rare and frequent mutation scenario ...“

Outlook Does understanding of life require more chemistry ? Thinking in terms of processes rather than structures !

The difficulty to define the notion of „gene”. Helen Pearson, Nature 441: 399-401, 2006

ENCODE Project Consortium. Identification and analysis of functional elements in 1% of the human genome by the ENCODE pilot project. Nature 447:799-816, 2007

ENCODE stands for ENCyclopedia Of DNA Elements.

Acknowledgement of support

Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No. 09942, 10578, 11065, 13093 13887, and 14898 Wiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF) Project No. Mat05 Jubiläumsfonds der Österreichischen Nationalbank Project No. Nat-7813 European Commission: Contracts No. 98-0189, 12835 (NEST) Austrian Genome Research Program – GEN-AU: Bioinformatics Network (BIN) Österreichische Akademie der Wissenschaften Siemens AG, Austria Universität Wien and the Santa Fe Institute

Universität Wien

Coworkers

Peter Stadler, Bärbel M. Stadler, Universität Leipzig, GE Paul E. Phillipson, University of Colorado at Boulder, CO Heinz Engl, Philipp Kügler, James Lu, Stefan Müller, RICAM Linz, AT Jord Nagel, Kees Pleij, Universiteit Leiden, NL Walter Fontana, Harvard Medical School, MA Christian Reidys, Christian Forst, Los Alamos National Laboratory, NM Ulrike Göbel, Walter Grüner, Stefan Kopp, Jaqueline Weber, Institut für Molekulare Biotechnologie, Jena, GE Ivo L.Hofacker, Christoph Flamm, Andreas Svrček-Seiler, Universität Wien, AT Kurt Grünberger, Michael Kospach , Andreas Wernitznig, Stefanie Widder, Stefan Wuchty, Universität Wien, AT Jan Cupal, Stefan Bernhart, Lukas Endler, Ulrike Langhammer, Rainer Machne, Ulrike Mückstein, Hakim Tafer, Thomas Taylor, Universität Wien, AT

Universität Wien

Web-Page for further information: http://www.tbi.univie.ac.at/~pks